Graham White: My Notes

Find the smallest number that can be expressed as
the sum of 25 consecutive prime numbers,
the sum of 99 consecutive prime numbers,
the sum of 189 consecutive prime numbers,
the sum of 467 consecutive prime numbers,
the sum of 535 consecutive prime numbers,
and is itself a prime number.

For example, 41 is the smallest prime number that can be expressed as
the sum of 3 consecutive primes (11 + 13 + 17 = 41) and
the sum of 6 consecutive primes (2 + 3 + 5 + 7 + 11 + 13 = 41).

sub primes {
  my $max = shift || 10;
  my @primes = ( 2, 3, 5, 7 );
  return @primes if ($max <= 9);
  my $loop = 9;
  while (scalar(@primes) < $max) {
    my $is_prime = 1;
    for (my $div = 3; $div < ($loop-1)/2; $div++) {
      $is_prime = 0 if ($loop % $div == 0);
    }
    push (@primes,$loop) if ($is_prime);
    $loop += 2;
  }
  return @primes;
}

use strict;
use FileHandle;

sub sum_primes {
  my $amount = shift;
  my $start = 0;
  my @sums;

  while ($amount < scalar(@_)) {
    my $sum = 0;
    for (my $i = $start; $i < $amount; $i++) {
      $sum += $_[$i];
    }
    push(@sums,$sum);
    $start++;
    $amount++;
  }
  return @sums;
}

sub read_primes {
  my $filename = shift;
  my $fh = new FileHandle;
  $fh->open($filename) || die "$filename: $!\n";
  my @primes;
  push(@primes,split) while (<$fh>);
  $fh->close();
  return @primes;
}

sub is_prime {
  my $num = shift;
  foreach my $prime (@_) {
    return 1 if ($num == $prime);
  }
  return 0;
}

my @primes = read_primes("1000000.txt");
my @sum_list;
push(@sum_list, sum_primes(25,@primes));
push(@sum_list, sum_primes(99,@primes));
push(@sum_list, sum_primes(189,@primes));
push(@sum_list, sum_primes(467,@primes));
push(@sum_list, sum_primes(535,@primes));
@sum_list = sort(@sum_list);
my $prev = 0;
my $same = 0;
foreach my $num (@sum_list) {
  if ($num == $prev) {
    $same++;
    if ($same == 4) {
      print "Found $num, checking... ";
      if (is_prime($num,@primes)) {
        print "PRIME! :-)\n";;
        last;
      } else {
        print "not prime :-(\n";
        $same = 0;
      }
    }
  } else {
    $same = 0;
  }
  $prev = $num;
}

Below is a diagram of a computer network. The nodes are hosts on the network, and the lines between them are links. A packet is sent out from host G with a destination of 201.89.136.112. Which nodes does the packet pass through on its way to the destination? (include start and final node in your answer)

Here is a random zip archive for you to download:
GoogleTreasureHunt08_15866755520722619948.zip

Unzip the archive, then process the resulting files to obtain a numeric result. You'll be taking the sum of lines from files matching a certain description, and multiplying those sums together to obtain a final result. Note that files have many different extensions, like '.pdf' and '.js', but all are plain text files containing a small number of lines of text.

Sum of line 4 for all files with path or name containing BCD and ending in .pdf
Sum of line 5 for all files with path or name containing mno and ending in .rtf
Hint: If the requested line does not exist, do not increment the sum.

Multiply all the above sums together and enter the product below.
(Note: Answer must be an exact, decimal representation of the number.)

#!/usr/bin/perl -w
use strict;
use File::Find;
use FileHandle;
my $total1 = 0;
my $total2 = 0;
find(\&wanted, ("/home/gwhite/GoogleTreasureHunt08_15866755520722619948"));
print $total1*$total2."\n";
sub wanted {
 return if (-d $File::Find::name);
 if (($File::Find::name=~m!BCD!i) && ($File::Find::name=~m!\.pdf$!i)) {
   my $fh = new FileHandle;
   $fh->open($File::Find::name) || die ($File::Find::name." Oops: $!\n");
   while (<$fh>) {
     last if ($fh->input_line_number>4);
     chomp($_);
     $total1+=$_ if ($fh->input_line_number==4);
   }
   $fh->close();
 }
 elsif (($File::Find::name=~m!mno!i) && ($File::Find::name=~m!\.rtf$!i)) {
   my $fh = new FileHandle;
   $fh->open($File::Find::name) || die ($File::Find::name." Oops: $!\n");
   while (<$fh>) {
     last if ($fh->input_line_number>5);
     chomp($_);
     $total2+=$_ if ($fh->input_line_number==5);
   }
   $fh->close();
 }
}

A robot is located at the top-left corner of a 65 x 61 grid (marked 'Start' in the diagram above)*.

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the not to scale diagram below).

How many possible unique paths are there?
(Note: Answer must be an exact, decimal representation of the number.)

#!/usr/bin/perl -w
use strict;
use Math::BigInt;
# change these to match your X & Y grid size
my $xgrid = 61;
my $ygrid = 65;
my $x = Math::BigInt->new($xgrid-1)->bfac();
my $y = Math::BigInt->new($ygrid-1)->bfac();
my $z = Math::BigInt->new($xgrid+$ygrid-2)->bfac();
print $z->bdiv($x->bmul($y))."\n";